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Cycling of the local interstellar matter
Adv. Space Res. Vol. 6, No. 2, pp. 109—118, 1986
0273—1177/86 80.00 + .50
Printed in Great Britain. All rights reserved.
Copyright
© COSPAR
CYCLING OF THE LOCAL INTERSTELLAR MATFER Kohji Tomisaka Tokyo Astronomical Observatory, University of Tokyo, Mitaka, Tokyo 181, Japan
ABSTRACT The origin of the local interstellar matter, especially the hot component, is studied. The bulk of the local interstellar space is occupied with hot low-density matter, which is similar to the gas heated by the shock front of the supernova remnant. We investigate the model that our Sun is located in a superbubble. The superbubbles are observed in Orion-Eridanus region and Gum nebula. The similar objects are found in /. 21 cm H I maps as H I shells and holes. The superbubbles certainly correlate with OB associations and giant molecular clouds. The evolution of superbubbles formed by sequential supernova explosions in an OB association is studied by hydrodynamical simulations. We compare the results with observations. A model of cycling of interstellar matter is presented, in relation to the evolution of the superbubble. 1. It~TTRODUCrION Our Sun is a moderately-aged star. Howøver, the environmental space surrounding our Sun has been found very active and young. The fact that the Sun is situated in such an active place, which would be accidental, enables us to understand the active nature of the interstellar medium by probing the local interstellar matter. 1.1
Obserwi~ons
Absorption line studies of the local interstellar medium (LISM) have revealed the H I distribution within 150 pc from the Sun. On this point, Bruhweiler /1/ has summarized the overall distribution of LISM as follows: (1) Outside the rather diffuse cloud ~H!~ 0.04-0.1 cnr~ in which the Sun is immersed, more low-density (hot) gas is found to be distributed upto the distance d~. pc. InThe number density in ~the d low-density region is cm~ 4 50. (2) the average more distant region (50 pc ~ 150 pc), most measured as i~j~~7x10 directions show significant absorption NH,1O’9cm2 towards stars with distances ‘75 Pc. However, low absorption regions toward which N~i~1018cm2are seen towards two directions: the north galactic pole (d~100-150 pc) and 13 CMa, i.e., (l,b)~(~5,O) (d~200 Pc). TABLE I Soft X-ray Background Radiation Authors
local hot region
Williamson et al./2/ Burstein et al. /3/ Hayakawa et al. /4/
loop I
Stern and Bowyer /6/ Fried et al. /7/ Davelaan et al. /8/
~1O6K -‘~106K + ~1O63K 1.5xIO6K (cosmic abundance) 1.lxlO6K (depleted abundance) 1066 K (NH<2x 10’9cm2) 105~56K~ ~1O6K 1065 K
Nousek et al.
106K
Hayakawa et al.
/5/
(NH=3x 1020cm2)
/9/
+
108 4K1
10847K (N
Schnopper et al./1O/
1.IxlO6K
Rocchia et al.
1.lxlO6K
/11/
20cm2) 3.8x1O~’K 8=(4_ 15)x 10 (NH=4x 1020cm2) +
6x1O6K
4.7xIO6K 1020cm2)
(NH=7x
$ EIJV background ~ disk-like halo component with Nij~3x1O20cm3 JASH 6:2—H
109
110
K. Tomisaka
The physical state of LISM is also obtained through the observation of X-ray/EIJV background radiation. Here, we briefly summarize the 4exp(-oN~ consensus of the observations. After subtracting the extragalactic component dN/dEocE~1),we can divide the soft X-ray background into two components: (1) homogeneous component of background radiation, and (2) the component associated with radio Loop I (or North Polar Spur). The physical quantities derived from observations are summarized in Table 1. 19cm2 ) hot gas with temperature .~,1O6K. This indicates the hot gas surrounds the Sunx10 immediately as a local The first component is emitted by anthat absorption-free (N8, several hot region, which seems to corresponds to the H I-deficient region with d~5O pc. The temperature of the second component is higher than the first one as T~’~1O65K. The column density of absorbing matter between the emitting re~ionand the Sun has been fitted in entirely different ways as NH,~2xI019cm2/5/,~3x102°cm2 /8-11/. 1.2 Origin of Hot Interstellar Matter Let us consider the origin of the hot gas observed in the local interstellar space: local hot region and that associated with Loop I. Theoretical models of interstellar matter by Cox and Smith /12/ and McKee and Ostriker /13/ have shown that a large fraction of interstellar space is heated-up by the shock fronts of supernova remnants (SNRs). Here, we pay attention to the problem whether the observed X-ray is explained by the emission from SNRs. Cox and Anderson /14/ have studied the X-ray emission from an ~4R expanding into low-density
hot medium. They intended to fit the observed properties of the X-ray from the local hot region. They have shown that observations of the soft X-ray background radiation by Wisconsin group /7/ in B-band (0.1-0.18 keV) and C-band (0.15-0.28 keY) are explained by the ~‘IRmodel with the parameters as follows: the explosion energy of a supernova, E 5° erg, the ambient density into which an SNR expands, no~_4x1O3cm3, the age, t~ 5yr, and 0=5x10 the size of the SNR, rsNp~.-SO--lO0pc. On the other hand, Hayakawa et al. /9/ 5~1O has concluded that X-ray from the inside of Loop I is fitted by an SNR model as Eo=2xlO50erg, no~4x103cm3 , tge~3x lO4yr , rSNR~4S pc, using the data of the X-ray spectrum and NH towards the galactic pole. The characteristic points common to the above two SNR models are that both SNRs are expanding into ~ery low-density medium as n~~4x103cm3and that SNRs are in the adiabatic phase, during which radiative cooling does not play an important role. The average total H I density is estimated by the IUE observation as nH,_~rO.4&m3 /15/. Even the intercloud density attains n,~,,-~-.0.Icm3 within d~1kpc /16/. On the other hand, the density into which the SNRs expand is lower than ~‘..1O~2cm3 . If it is not the case that the local interstellar matter is intrinsically very low-density, how this low-density material is supplied? 2. LISM AS A SUPERBUBBLE If’ soft X-ray is due to the SNRs with the size of 50
-
100 pc, the size of
the
low—density
space into which the SNR expands would exceed ~ 100 - 200 Pc or more. A proper candidate which can form such a large-size low-density hot region is a superbubble. Three examples of them are known by now. Observational quantities of superbubbles are summarized in Table 2. They have large size r 150 pc, and are associated with H I shell and soft X-ray emission, which seems us to indicate that X-ray emitting hot gas is surrounded by the H I shell. TABLE 2 Observed Results of Three Candidates of Superbubble Object
X-ray
Orion-Eridanus (2-3)xlO6K Gum nebula ? Cygnus Superbubble 2x 106 K
He
H I
d(pc)*
E~(erg)”
OB association
Yes Yes Yes
Yes Yes Yes
280 250 450
3x1052 5x1O~ 1052 454 ~
On OB I ~ Vel Cyg OB 2
d and Ko denote respectively, the diameter and the estimated ejection energy. t Reynolds and Ogden /17/, ~ Reynolds /18/, ~ Cash et al. /19/.
*
Objects of the same kind are found from the He÷ ( N II ) plates of the Large Magellanic Cloud and the Small Magellanic Cloud by Meaburn and his colaborators /20/. They listed about 100 giant shells whose diameters are in the range of 20 — 280 pc and about 10 supergiant shells whose diameters reach I kpc. The supergiarit shells coincide with regions which are devoid of neutral hydrogen and contains many 0, B stars. From (S II) /H a line ratios, Georgelin et al. /21/ have concluded that these ionized bubbles are most probably old H II regions inside which supernova explosions have occurred. Surveys also have been done by ~. 21
Cycling of the LISM
111
cm H I map in search of H I shells and holes /28/. Although it has not been cleared whether the HI shells are associated with other objects due to heavy obscuration in the disk of our Galaxy /28/, this difficulty is overcome by the survey of the H I holes in M 31. Brinks and Bajaja /23/ have listed up 141 H I holes with diameter 2O0pc~d75Opc in M31. They have been shown that there is more overlapping between H I holes and 08 associations than would be expected if there were no correlation at all. We can easily suppose that the superbubbles are formed by sequential explosions of supernovae in OB associations and/or cooperative stellar winds from early type stars in OB associations. A pre-existing SMR or a stellar wind bubble is reactivated by new explosion of supernova in it and expands further. This model has been studied by Bruhweiler et al./24/ and Tomisaka et al. /25/. Recently the effect of the density stratification in the galactic disk to the evolution of superbubbles has been examined by Tomisaka and Ikeuchi /26/. In the next section, the results of these hydrodynamical simulations are shown. 3. EVOLUTION OF THE SUPERBUBBLE 3.1 Model Based on the model that the energy source of superbubbles consists in OB association, the supernova rate in an OB association is one of the most important parameters. We begin with the estimation of the supernova explosion rate, S0g . It has been estimated as 6yr~ from the supernova rate in our Galaxy under the assumption that all ,Soa=1/AT.’..(1-5)xIO the type II supernovae originate in massive stars /25/. Further, Cowie et al. /Z7/ have derived the explosion rate in an OB association with using the number of early-type stars within the association as ~ These two estimates agree with each other. Estimating the time variation of supernova rate by the Salpeter’s initial mass function and data of stellar-lifetime calculation compiled by Larson /28/, we find the supernova rate nearly constant upto ~,4Q73yr, at which the star with 10 H® ends its life. Therefore, we assume S 6yr~ constant throughout in the present paper. 0g=5x1O The kinetic luminosity inferred from the above supernova explosion rate is oinS E LSNS0gE0~I.6x1O~(>~ ~ ~ ) erg s1, (I) lsr 10 erg with the energy of a supernova explosion E 0. On the other hand, the total stellar wind luminosity emitted from early typ~ stars in an OB association has been estimated by Bruhweiler et al. /24/ for typical one (Sco OBI) as L~=N~ü ~ I~I V~ 28
10-6M®yr ~
~ 2x1&kms
)2
erg s~,
(2)
where N
)l/3~
3cm3 43(±!~L)l/3( (3) IOM® 10~Cau )_l/3 ~ where Mej means the mass ejected from supernova. The shock front reaches the shell of the pre-existing SNR, whose radius is denoted by r~~ji , after T~
3”Iej
4itpm~jn~~v
S
.
X in4 (.a\5/2f ~
i~.ipc
~
E~ 1051 erg
\—l/2, ~ ~
flca:,
10 ~cm
\l/2 ,
yr.
between supernovae, At, so that average superbubble (-‘~ 3/4) is observed in the state after the shock front reaches shell. Because the density in the cavity is low, the newly formed SNR does not enter radiative phase and the cooled shell is never formed in the pre-existing cavity. New raise the pressure in the cavity. Thus, the shell expands further. This timescale r is shorter than the mean interval
the the the 9~1R
The structure of the superbubble formed in the homogeneous interstellar medium with no=0.1cm3 is shown in Figure 1; t~4.8x106 yr have passed after the sequential supernova explosions start. The shell reaches r 5450 pc. The superbubble is characterized by hot large
112
K. Tomisaka
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Cycling of the LISM
113
6K, n 3cm3 surrounded by cooled shell with density -‘-Icnf3. 4.5)4.-’~2x1O 05-’~2x10 Further, we have found from the numerical results that the shell of the superbubble expands according to the expansion law as (5) 10 yr The bubble ends its life when the shell is decelerated to the random velocity of the interstellar clouds c8km s~ or the power of the sequential explosion in an 08 association falls off. The latter time scale, tOB is estimated from the mass function of stars in the 08 association as (I—3)x ~ yr. The lifetime of superbubble and their final size are given as cavity with T
,
t
,
,
7 (—~—_3 y°46yrj 0. 1cm
5505=min [ t,j~, 2.4x i0
(6)
r
no 3)(~),470( no (7) 0.1cm 7 yr, the bubble can lOyr expand to r 0.1cm 3 ) - 315 Pc (no=O.1 cm3 ). If For t t06o10 7 yr, the maximum4.~I6O size becomes pc (no=1 as cm r 3 ) - 470 pc (no-O.1 08 is cm3 as long ). as 3x10 50 163 pc (no-I cm 5t0~=min[3I5(
3.3
Effect of the Scale-Height of the Interstellar Hatter
Because the exponential scale-height of H I gas is about 140 pc /15/, the evolution of superbubbles with radius larger than 150 pc should be affected by the density distribution. Here we pay attention to this effect. The density distribution perpendicular to the galactic disk is taken from the model by Fuchs and Thielheini /29/, in which H I gas consists in two parts: cloud component (Gaussian distribution with scale height h~110 pc) and intercloud component (exponential distribution with h~ 250 pc). We study the evolution of the superbubble in this density distribution. A typical result is shown in Figure 2. This shows the case that the density at the disk plane, n(z=0)=Icm3 and the height of an OB association from the disk plane, z~g—I00pc- In Figure 2, we plot the pressure contour of the bubble at the stage of t=1.5x 106 yr (a), t=4.5x 106 yr (b), and t=9,5x 106 yr (C). Because it is easier to expand into the low-density direction, the elongation in the z-direction is clearly seen after the size of the bubble surpasses the scale height of the disk. On the other hand, in the case of n(z=0)-Icm3 and ZOB”rOpc, we have found that the anlsotro?pY in expansion is very weak and the shell expands almost spherically (Figure 3; t=1.05<10 yr). This is because the dynamical suppression and the effective cooling both due to high density cooperatively works not to expand till the scale-height of the disk.
,
The effect of the density stratification is more essential to the case of low ambient density, because the shell reaches more easily the scale—height. We show the result of n(z=0)=0.3cm3 and ZOB=IOO pc in Figure 4. In this case, we take account of the thermal conduction. As the thermal conduction coefficient, we employ the classical conduction coefficient
derived by Spitzer /30/ as ,c-6x107T25erg cm~ 5H
-
Thermal conduction plays an
important role in the hot cavity and the temperature in the cavity becomes constant due to n the model, hot low-density matterrarefied spreads over rapid 63K, heat transport.3. Based The on cavity is the occupied with hot gas as 200 PC lfl radial direction and 400 - 500 pc in the z-direction. T0a5010 5)5o2xI0~cm 3.4
X-ray from Superbubble
The hot gas contained in the cavity of the superbubble with temperature T 63 K is able to emit soft X-ray. We estimate the surface brightness of the X-ray from 4.5)5-’-10 the bubble using the band emissivity derived by Raymond et al. /31/ JBund-)~fA8and(T, a )n2ds.
(8)
We show in Figure 5 the surface brightness in two bands: L-band (0.155 - 0.284 keV) and N-band (0.5~ - 0.873 keY). The predicted surface brightness from this model is -‘-IO8erg s~ cm2 srt in L-band and -‘-3x lO9erg s~ cm2 sr~ in ft-band. Although this corresponds to the value observed from outside the bubble, the surface brightness received in the bubble would not be largely different from that observed from outside. On the other hand, the observed counts rates by Wisconsin’s group /14/, 80 - 200 counts s~ (in L-band), and 30 - 50 counts s~ (in H-band), are deconvolved to the intrinsic surface brightness with use of the effective area data /7/ as (5—13)xlO9erg s~ cm2 sr1 (in L-band), and (1—2)x IO8erg ~ cm2 sr~ (in M-band). Compared between the observation and the model, although the surface brightness in M-band is not sufficiently explained about factor 3, X-ray in L-band is well explained as the superbubble origin. We conclude that the soft X-ray
114
K. Tomisaka
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-
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3
Fig. 5. The surface brightness of X—ray emitted from the hot gas contained in the cavity of the superbubble. This is the case of n(z0)’0.3 cm3 and zoB=lOO pc. The surface brightness in L—band (0.155—0.284 key) and M—band (0.533—0.873 key) are are plotted in (a) and (b), respectively.
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-t ~0
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flo
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Fig. 6. Constraints on the fl-T plane by the conditions: LX ~ erg s-1, 1~> ~ K, and E
los
116
K. Tomisaka
background radiation is emitted from the local superbubble as well as the Sun.
the
SNR
surrounding
4. DISCUSSION
4.1 Excess X-ray Emission from the Galactic Ridge in 2
-
Ii keV Band
SNRs exploding in the cavity of superbubble are characterized by (1) a young age as yr (equation (4)) and (2) high temperature of the post-shock gas as ~
K.
(9)
The excess emission from the galactic ridge in the energy band of 2 — 10 keY, which was pointed out by Worrall et al. with the data of HEAO I /32/, has been reinvestigated by HEAO 2, EXEXSAT, and Tenma satellite /33/. It is found that the total luminosity in 2-11 key in our Galaxy attains ~~1038erg s~ - Because highly ionized iron line was detected by Tenma satellite, the excess emission is confirmed from hot gas with temperature -‘-1 keY. The proper candidate is a young SNR. However, radio SNRs or other feature related to SNRs are not observed in the field of view. Here, we discuss the model that the excess emission is from the /34/. For the early SNR to escape from radio survey, the radio lower than the detection toward the galactic i.e., The theoretical model limit for the surface brightnessridge, - diameter established. Thus, we use the empirical E—D relation explicitly density a /35/ as E(1GHz)~~2.88x104(.j~P.~_y38 n2
SNRs born in superbubbles surface brightness should be20Wm2 Hz~sr1 E(1GHz)~10 (1—D) relation has not been depending on the ambient
W m~2 Hz~ sr*
(10)
We plot in Figure 6 the region for age r, and the ambient density a which satisfies the condition Lx~1033 erg s~,T 7 K, and E’i1020W m2 Hz-I sr~ - SNRs in the low-density region as n-’-0.01 cm3 emits 4.10 the X-ray of 1O~ erg s~ during -‘-3x104 yr with radio surface brightness ~i1O’-0Wm~Hz~sr1 - Total luminosity emitted in 1.5 -25 keY in our galaxy becomes
Lx~iO.5x I 0~
erg s1 (for flQ .01 cm3),
(11)
where At is the mean interval of supernova explosions in our galaxy. We can conclude that ~Rs expanding in tenuous medium like a cavity of the superbubble fall below the detection limits of current radio surveys but still contribute significantly to the observed X-ray flux in the 2 - 11 keY band, if the supernova rate is as one per 10 years. 4.2 Picture of the Cycling of LLS’-I From the results of the numerical simulation on the superbubble, it has been found that the hot gas around our Sun seems to be a part of the cavity of a superbubble. The superbubbles are formed by the energy emitted from OB associations. It is observationally confirmed that 08 associations are associated with giant molecular clouds or molecular cloud complexes /36/. Further, the early type stars in the 08 association are formed in the giant molecular cloud in consequence of active early-type-star formation in it /37/. OB associations and giant molecular clouds are concentrated on spiral arms in the galaxy /38/. The ‘density wave promotes the coagulation of small clouds into large cloud complexes by what appears to be a combination of collisional agglomeration and large-scale gravitational instabilities /39/. This explains naturally the distribution of giant molecular clouds, because clouds are gathered into the spiral arms and giant molecular clouds are formed in the arms by collisional agglomeration and instabilities. type stars in OB associations formed by active star formation in giant molecular clouds explode sequentially as type II supernovae after several millions years have passed. Giant molecular clouds are destroyed under the influence of the active star formation, in
Early
the time scale --.io~ yr /40/. The formed 08 association emits large energy in the form of supernova explosions in -..(I--3)x io~ yr. In consequence, the interstellar matter in the vicinity of the OB association is heated-up by the shock fronts of SNRs. After that, the supernova rate decreases due to the relatively long lifetime of intermediate-mass stars. The superbubble does not expands further. After the active phase of the the heated matter return to the stancklrd interstellar matter?
superbubble,
how
does
The cooling time of hot gas in the cavity is estimated as
5/2xn
2 ~ 5O0kT An
8~
a
—I
(-j~~) yr. T .6
12
Cycling of the LISM
117
This is somewhat longer than the time necessary for interstellar matter to travel from one arm to the other arm tc;r-7r/(cZ~-qp)=2.7x108 yr, with the standard two-arm spiral model (the pattern velocity, Q~,=13.5km s kpc~, and the rotation velocity, 9-24.7km s~ kpc~). The superbubble should be destroyed by other processes: (1) Interstellar clouds permeate the cavity of the bubble and eventually fill up it. This timescale is expressed with the random velocity of clouds, v~j, as — r~ 3xIO~~—~—--’’ Vrar4 \-.J 3 1”8kni s~’ yr. c1— “200Pc (2) Galactic differential rotation deforms the shape of the bubble and squashes it. This phenomenon occurs in a timescale of ~
(14)
where R represents the distance from the galactic center, -‘- 10 kpc. Because the latter two timescales, t~ 1, and t~104.~ , are much smaller than ~ , the local interstellar matter will be mixed with the interstellar matter outside the bubble before reaching the next arm. Thus, the interstellar matter repeats the cycle. The author would like to acknowledge Professors S. Sakashita, Y. Uchida, and S. Ikeuchi for their encouragement. He also acknowledge Yamada Science Foundation and Nukazawa Memorial Foundation (Hokkaido University) for travel support. The numerical calculation was performed by HITAC M28O-H/t~200-Hat the Computing Center, Hokkaido University and FACON M38O-R at Tokyo Astronomical Observatory. This work was supported in part by Grant-in—Aid for Encouragement of Young Scientists from the Ministry of Education, Science, and Culture (61790072). He also acknowledges the JSPS Fellowships for Japanese Junior Scientists for financial aid (FY 1966).
REFERENCES 1. F. C. Bruhweiler, in IAU Colloquium No 81, Local Interstellar Matter, ed. by F. C. Bruhweiler, Y. Kondo, and B. D. Savage (NASA Conference Publication) 1984. 2. F. 0. Williamson, W. T. Sanders, W. L. Kraushaar, D. McCammon, R. Borken, and A. N. Bunner, Astrophys. J. Letters, 193, L133 (1974). 3. P. Burstein, R. J. Borken, W. L. Kraushaar, and W. T. Sanders, Astrophys. J., 213, 405 (1977). 4. S. Hayakawa, T. Kato, F. Nagase, K. Yainashita, and Y. Tanaka, Astrort. Astrophys., 62, 21 (1978). 5. S. Hayakawa, T. Kato, F. Nagase, K. Yamashita, and Y. Tanaka, Publ. Astron. Soc. Japan, 31, 71 (1979).
6. R. Stern, and S. Bowyer, Astrophys. J., 230, 755 (1979). 7. p. M. Fried, J. A. Nousek, W. T. Sanders, and W. L. Kraushaar, Astrophys. J., 242, 987 (1980). 8. J. Davelaan, J. A. M. Bleeker, A. J. M. Deerenberg, Astron. Astrophys., 92, 231 (1980). 9. J. A. Nousek, p. N. Fried, W. T. Sanders, W. L. Kraushaar, Astrophys. J., 298, 83 (1992). 10. H. W. Schnopper, J. P. Delvaille, R. Rocchia, C. Blondel, C. Cheron, J. C. Christy, R. Ducros, L. Koch, and R. Rotherflug, Astrophys. J., 293, 131 (1992). II. R. Rocchia, M. Arnaud, C. Blondel, C. Cheron, J. C. Cristy, R. Rothenflug, H. W. Schnopper, and J. P. Delvaille, Astron. Astrophys., 130, 53 (1984). 12. D. P. Cox, and B. W. Smith, Astrophys. J. Letters, 189, L105 (1974) 13. C. F. McKee, and J. P. Ostriker, Astrophys. J., 218, 148 (1977). 14. D. P. Cox, and P. R. Anderson, Astrophys. J., 293, 268 (1992). 15. J. M. Shull, and N. E. Van Steenberg, Astrophys. J., 294, 599 (1985). 16. L. Spitzer, Jr., Physical Processes in the Interstellar Medium, Wiley-Interscience, New York, 1978. -17. R. J. Reynolds, and P. M. Ogden, Astrophys. J., 229, 942 (1979). 18. R. J. Reynolds, Astrophys. J., 206, 679 (1975). 19. W. Cash, P. Charles, S. Bowyer, F. Walter, G. Garmire, C. Riegler, Astrophys. J. Letters, 238, L71 (1980). 20. J. Meaburn, Monthly. Notices Roy. Astrort. Soc., 192, 365 (1980) 21. Y. M. Georgelin, Y. P. Georgelin, A. Laval, 0. Monnet, and H. Mosado, Astron. Astrophys. Supp 1., 54, 459 (1983). 22. C. Heiles Astrophys. J., ~, 533 (1979). Astrophys. J. Suppi., ~, 585 (1984). 23. E. Brinks, and E. Ba.jaja, submitted to Astron. Astrophys. (1986). 24. F. C. Bruhweiler, 1. R. Gull, M. Kafatos, and S. Sofia, Astrophys. J. Letters, 238, 127 (1980). 25. K. Tomisaka, A. Habe, and S. Ikeuchi, Astrophys. Space Sci., 78, 273 (1981).
118
K. Tomisaka
26. K. Tomisaka, and S. Ikeuchi, Pubi. Astron. Soc. Japan in press (1986). 27. L. L. Cowie, E. H. Hu, W. Taylor, and D. 0. York, Astrophys. J. Letters, 290, L25 (1981). 22. R. B. Larson, Monthly. Notices. Roy. Astro. Soc., 166, 585 (1973) 29. B. Fuchs, and K. 0. Thielheim, Astrophys. J., ~7, 801 (1979). 30. L. Spitzer, Jr., Physics of Fully Ionized Gases, Wiley-Interscience, New York, 1982. 31. J. C. Raymond, D. P. Cox, and B. W. Smith, Astrophys. J., 205, 290 (1976). 32. D. M. Worrall, F. E. Marshall, E. A. Boldt, and J. H. Swank, Astrophys. J., 265, 111 (1992). 33. S. M. Kahn, and J.—P. Caillault, Astrophys. J., 305, 526 (1986) (the results by HEAO 2). R. S. Warwick, M. J. L. Turner, M. 0. Watson, and R. Willingale, Nature, 317, 218 (1985) (the results by EXOBAT). K. Koyama, K. Makishima, Y. Tanaka, and H. Tsunemi, Publ. Astron. Soc. Japan in press (1986) (the results by Tenma). 34. K. Koyama, S. Ikeuchi, and K. Tomisaka, Publ. Astron. Soc. Japan in press (1986). 35. K. Toinisaka, A. Habe, and S. Ikeuchi, Prog. Theor. Phys., 64, 1587 (1980). 36, L. Britz, Ph. D. Thesis Columbia University (NASA Technical Memorandum 79708), 1978. 37. B. 0. Elmegreen, and C. J. Lada, Astrophys. J., 214, 725 (1977). 38. F. J. Lockinan, Astrophys. J., 232. 761 (1979) (for distribution of H II regions). P. H. Solomon, D. B. Sanders, and A. R. Rivolo, Astrophys. J. Letters, 292, L19 (1985) (for molecular clouds). 39. B. 0. Elmegreen, in IAU Symposium No. 115 ‘Star Forming Regions, ed. by H. Peimbert and J. Jugaku, Reidel, Dordrecht, 1986. K. Tomisaka, Publ. Astron. Soc. Japan, 38, 95 (1986) and references therein. 40. F. Bash, M. Hausman, and J. Papaloizou, Astrophys. J., 245, 92 (1981).
0273—1177/86 80.00 + .50
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Copyright
© COSPAR
CYCLING OF THE LOCAL INTERSTELLAR MATFER Kohji Tomisaka Tokyo Astronomical Observatory, University of Tokyo, Mitaka, Tokyo 181, Japan
ABSTRACT The origin of the local interstellar matter, especially the hot component, is studied. The bulk of the local interstellar space is occupied with hot low-density matter, which is similar to the gas heated by the shock front of the supernova remnant. We investigate the model that our Sun is located in a superbubble. The superbubbles are observed in Orion-Eridanus region and Gum nebula. The similar objects are found in /. 21 cm H I maps as H I shells and holes. The superbubbles certainly correlate with OB associations and giant molecular clouds. The evolution of superbubbles formed by sequential supernova explosions in an OB association is studied by hydrodynamical simulations. We compare the results with observations. A model of cycling of interstellar matter is presented, in relation to the evolution of the superbubble. 1. It~TTRODUCrION Our Sun is a moderately-aged star. Howøver, the environmental space surrounding our Sun has been found very active and young. The fact that the Sun is situated in such an active place, which would be accidental, enables us to understand the active nature of the interstellar medium by probing the local interstellar matter. 1.1
Obserwi~ons
Absorption line studies of the local interstellar medium (LISM) have revealed the H I distribution within 150 pc from the Sun. On this point, Bruhweiler /1/ has summarized the overall distribution of LISM as follows: (1) Outside the rather diffuse cloud ~H!~ 0.04-0.1 cnr~ in which the Sun is immersed, more low-density (hot) gas is found to be distributed upto the distance d~. pc. InThe number density in ~the d low-density region is cm~ 4 50. (2) the average more distant region (50 pc ~ 150 pc), most measured as i~j~~7x10 directions show significant absorption NH,1O’9cm2 towards stars with distances ‘75 Pc. However, low absorption regions toward which N~i~1018cm2are seen towards two directions: the north galactic pole (d~100-150 pc) and 13 CMa, i.e., (l,b)~(~5,O) (d~200 Pc). TABLE I Soft X-ray Background Radiation Authors
local hot region
Williamson et al./2/ Burstein et al. /3/ Hayakawa et al. /4/
loop I
Stern and Bowyer /6/ Fried et al. /7/ Davelaan et al. /8/
~1O6K -‘~106K + ~1O63K 1.5xIO6K (cosmic abundance) 1.lxlO6K (depleted abundance) 1066 K (NH<2x 10’9cm2) 105~56K~ ~1O6K 1065 K
Nousek et al.
106K
Hayakawa et al.
/5/
(NH=3x 1020cm2)
/9/
+
108 4K1
10847K (N
Schnopper et al./1O/
1.IxlO6K
Rocchia et al.
1.lxlO6K
/11/
20cm2) 3.8x1O~’K 8=(4_ 15)x 10 (NH=4x 1020cm2) +
6x1O6K
4.7xIO6K 1020cm2)
(NH=7x
$ EIJV background ~ disk-like halo component with Nij~3x1O20cm3 JASH 6:2—H
109
110
K. Tomisaka
The physical state of LISM is also obtained through the observation of X-ray/EIJV background radiation. Here, we briefly summarize the 4exp(-oN~ consensus of the observations. After subtracting the extragalactic component dN/dEocE~1),we can divide the soft X-ray background into two components: (1) homogeneous component of background radiation, and (2) the component associated with radio Loop I (or North Polar Spur). The physical quantities derived from observations are summarized in Table 1. 19cm2 ) hot gas with temperature .~,1O6K. This indicates the hot gas surrounds the Sunx10 immediately as a local The first component is emitted by anthat absorption-free (N8, several hot region, which seems to corresponds to the H I-deficient region with d~5O pc. The temperature of the second component is higher than the first one as T~’~1O65K. The column density of absorbing matter between the emitting re~ionand the Sun has been fitted in entirely different ways as NH,~2xI019cm2/5/,~3x102°cm2 /8-11/. 1.2 Origin of Hot Interstellar Matter Let us consider the origin of the hot gas observed in the local interstellar space: local hot region and that associated with Loop I. Theoretical models of interstellar matter by Cox and Smith /12/ and McKee and Ostriker /13/ have shown that a large fraction of interstellar space is heated-up by the shock fronts of supernova remnants (SNRs). Here, we pay attention to the problem whether the observed X-ray is explained by the emission from SNRs. Cox and Anderson /14/ have studied the X-ray emission from an ~4R expanding into low-density
hot medium. They intended to fit the observed properties of the X-ray from the local hot region. They have shown that observations of the soft X-ray background radiation by Wisconsin group /7/ in B-band (0.1-0.18 keV) and C-band (0.15-0.28 keY) are explained by the ~‘IRmodel with the parameters as follows: the explosion energy of a supernova, E 5° erg, the ambient density into which an SNR expands, no~_4x1O3cm3, the age, t~ 5yr, and 0=5x10 the size of the SNR, rsNp~.-SO--lO0pc. On the other hand, Hayakawa et al. /9/ 5~1O has concluded that X-ray from the inside of Loop I is fitted by an SNR model as Eo=2xlO50erg, no~4x103cm3 , tge~3x lO4yr , rSNR~4S pc, using the data of the X-ray spectrum and NH towards the galactic pole. The characteristic points common to the above two SNR models are that both SNRs are expanding into ~ery low-density medium as n~~4x103cm3and that SNRs are in the adiabatic phase, during which radiative cooling does not play an important role. The average total H I density is estimated by the IUE observation as nH,_~rO.4&m3 /15/. Even the intercloud density attains n,~,,-~-.0.Icm3 within d~1kpc /16/. On the other hand, the density into which the SNRs expand is lower than ~‘..1O~2cm3 . If it is not the case that the local interstellar matter is intrinsically very low-density, how this low-density material is supplied? 2. LISM AS A SUPERBUBBLE If’ soft X-ray is due to the SNRs with the size of 50
-
100 pc, the size of
the
low—density
space into which the SNR expands would exceed ~ 100 - 200 Pc or more. A proper candidate which can form such a large-size low-density hot region is a superbubble. Three examples of them are known by now. Observational quantities of superbubbles are summarized in Table 2. They have large size r 150 pc, and are associated with H I shell and soft X-ray emission, which seems us to indicate that X-ray emitting hot gas is surrounded by the H I shell. TABLE 2 Observed Results of Three Candidates of Superbubble Object
X-ray
Orion-Eridanus (2-3)xlO6K Gum nebula ? Cygnus Superbubble 2x 106 K
He
H I
d(pc)*
E~(erg)”
OB association
Yes Yes Yes
Yes Yes Yes
280 250 450
3x1052 5x1O~ 1052 454 ~
On OB I ~ Vel Cyg OB 2
d and Ko denote respectively, the diameter and the estimated ejection energy. t Reynolds and Ogden /17/, ~ Reynolds /18/, ~ Cash et al. /19/.
*
Objects of the same kind are found from the He÷ ( N II ) plates of the Large Magellanic Cloud and the Small Magellanic Cloud by Meaburn and his colaborators /20/. They listed about 100 giant shells whose diameters are in the range of 20 — 280 pc and about 10 supergiant shells whose diameters reach I kpc. The supergiarit shells coincide with regions which are devoid of neutral hydrogen and contains many 0, B stars. From (S II) /H a line ratios, Georgelin et al. /21/ have concluded that these ionized bubbles are most probably old H II regions inside which supernova explosions have occurred. Surveys also have been done by ~. 21
Cycling of the LISM
111
cm H I map in search of H I shells and holes /28/. Although it has not been cleared whether the HI shells are associated with other objects due to heavy obscuration in the disk of our Galaxy /28/, this difficulty is overcome by the survey of the H I holes in M 31. Brinks and Bajaja /23/ have listed up 141 H I holes with diameter 2O0pc~d75Opc in M31. They have been shown that there is more overlapping between H I holes and 08 associations than would be expected if there were no correlation at all. We can easily suppose that the superbubbles are formed by sequential explosions of supernovae in OB associations and/or cooperative stellar winds from early type stars in OB associations. A pre-existing SMR or a stellar wind bubble is reactivated by new explosion of supernova in it and expands further. This model has been studied by Bruhweiler et al./24/ and Tomisaka et al. /25/. Recently the effect of the density stratification in the galactic disk to the evolution of superbubbles has been examined by Tomisaka and Ikeuchi /26/. In the next section, the results of these hydrodynamical simulations are shown. 3. EVOLUTION OF THE SUPERBUBBLE 3.1 Model Based on the model that the energy source of superbubbles consists in OB association, the supernova rate in an OB association is one of the most important parameters. We begin with the estimation of the supernova explosion rate, S0g . It has been estimated as 6yr~ from the supernova rate in our Galaxy under the assumption that all ,Soa=1/AT.’..(1-5)xIO the type II supernovae originate in massive stars /25/. Further, Cowie et al. /Z7/ have derived the explosion rate in an OB association with using the number of early-type stars within the association as ~ These two estimates agree with each other. Estimating the time variation of supernova rate by the Salpeter’s initial mass function and data of stellar-lifetime calculation compiled by Larson /28/, we find the supernova rate nearly constant upto ~,4Q73yr, at which the star with 10 H® ends its life. Therefore, we assume S 6yr~ constant throughout in the present paper. 0g=5x1O The kinetic luminosity inferred from the above supernova explosion rate is oinS E LSNS0gE0~I.6x1O~(>~ ~ ~ ) erg s1, (I) lsr 10 erg with the energy of a supernova explosion E 0. On the other hand, the total stellar wind luminosity emitted from early typ~ stars in an OB association has been estimated by Bruhweiler et al. /24/ for typical one (Sco OBI) as L~=N~ü ~ I~I V~ 28
10-6M®yr ~
~ 2x1&kms
)2
erg s~,
(2)
where N
)l/3~
3cm3 43(±!~L)l/3( (3) IOM® 10~Cau )_l/3 ~ where Mej means the mass ejected from supernova. The shock front reaches the shell of the pre-existing SNR, whose radius is denoted by r~~ji , after T~
3”Iej
4itpm~jn~~v
S
.
X in4 (.a\5/2f ~
i~.ipc
~
E~ 1051 erg
\—l/2, ~ ~
flca:,
10 ~cm
\l/2 ,
yr.
between supernovae, At, so that average superbubble (-‘~ 3/4) is observed in the state after the shock front reaches shell. Because the density in the cavity is low, the newly formed SNR does not enter radiative phase and the cooled shell is never formed in the pre-existing cavity. New raise the pressure in the cavity. Thus, the shell expands further. This timescale r is shorter than the mean interval
the the the 9~1R
The structure of the superbubble formed in the homogeneous interstellar medium with no=0.1cm3 is shown in Figure 1; t~4.8x106 yr have passed after the sequential supernova explosions start. The shell reaches r 5450 pc. The superbubble is characterized by hot large
112
K. Tomisaka
~
.,.~
~a)4J4~) 0~5 a~ U) .l-~>, ~ .0 5)
,~.4 ‘-‘~— r,00-
_____________________________ -~ ~— .: ~ ‘.4 .—.-‘,—.~-~ .4)0—>
U)>>’—
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2
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______
__________
—
U)
U’
—a)
——‘U— -4.-”‘U)’”-’
~. ‘UP0—) -.—”” ~
—, I
_________________
_________
.~:
~!
‘4-4 ~——--~
______
“
4)0d
—
U)
‘
““~
.4 a)
— ‘U
Qw0)w
,-4U)U.0 U))) 0 5) 5) 4) ,-1 .0 >~ ~ U) (5 (5 4) 0) )J ‘4-4 0 4)
5)004)0 5) 5) (5 -i U) ,_4 0.0 0 4) 4-i X OU)0O) .5) 0)0)4)’(5 C’4dU) 0011 •U)4~.0O4U)
0’~d 0’ 5)— .d .0 4-1 .~4 U) C .0
c
~ d/d(~w2)s
~ ‘b
C I>,
~iET:~
1’-’
0 0 - 0 .0 5) ‘a) 0 0U)4-’0)0 ,4 ‘4-i 0 0) 0) U) 0a) a) 4)5).))
Cycling of the LISM
113
6K, n 3cm3 surrounded by cooled shell with density -‘-Icnf3. 4.5)4.-’~2x1O 05-’~2x10 Further, we have found from the numerical results that the shell of the superbubble expands according to the expansion law as (5) 10 yr The bubble ends its life when the shell is decelerated to the random velocity of the interstellar clouds c8km s~ or the power of the sequential explosion in an 08 association falls off. The latter time scale, tOB is estimated from the mass function of stars in the 08 association as (I—3)x ~ yr. The lifetime of superbubble and their final size are given as cavity with T
,
t
,
,
7 (—~—_3 y°46yrj 0. 1cm
5505=min [ t,j~, 2.4x i0
(6)
r
no 3)(~),470( no (7) 0.1cm 7 yr, the bubble can lOyr expand to r 0.1cm 3 ) - 315 Pc (no=O.1 cm3 ). If For t t06o10 7 yr, the maximum4.~I6O size becomes pc (no=1 as cm r 3 ) - 470 pc (no-O.1 08 is cm3 as long ). as 3x10 50 163 pc (no-I cm 5t0~=min[3I5(
3.3
Effect of the Scale-Height of the Interstellar Hatter
Because the exponential scale-height of H I gas is about 140 pc /15/, the evolution of superbubbles with radius larger than 150 pc should be affected by the density distribution. Here we pay attention to this effect. The density distribution perpendicular to the galactic disk is taken from the model by Fuchs and Thielheini /29/, in which H I gas consists in two parts: cloud component (Gaussian distribution with scale height h~110 pc) and intercloud component (exponential distribution with h~ 250 pc). We study the evolution of the superbubble in this density distribution. A typical result is shown in Figure 2. This shows the case that the density at the disk plane, n(z=0)=Icm3 and the height of an OB association from the disk plane, z~g—I00pc- In Figure 2, we plot the pressure contour of the bubble at the stage of t=1.5x 106 yr (a), t=4.5x 106 yr (b), and t=9,5x 106 yr (C). Because it is easier to expand into the low-density direction, the elongation in the z-direction is clearly seen after the size of the bubble surpasses the scale height of the disk. On the other hand, in the case of n(z=0)-Icm3 and ZOB”rOpc, we have found that the anlsotro?pY in expansion is very weak and the shell expands almost spherically (Figure 3; t=1.05<10 yr). This is because the dynamical suppression and the effective cooling both due to high density cooperatively works not to expand till the scale-height of the disk.
,
The effect of the density stratification is more essential to the case of low ambient density, because the shell reaches more easily the scale—height. We show the result of n(z=0)=0.3cm3 and ZOB=IOO pc in Figure 4. In this case, we take account of the thermal conduction. As the thermal conduction coefficient, we employ the classical conduction coefficient
derived by Spitzer /30/ as ,c-6x107T25erg cm~ 5H
-
Thermal conduction plays an
important role in the hot cavity and the temperature in the cavity becomes constant due to n the model, hot low-density matterrarefied spreads over rapid 63K, heat transport.3. Based The on cavity is the occupied with hot gas as 200 PC lfl radial direction and 400 - 500 pc in the z-direction. T0a5010 5)5o2xI0~cm 3.4
X-ray from Superbubble
The hot gas contained in the cavity of the superbubble with temperature T 63 K is able to emit soft X-ray. We estimate the surface brightness of the X-ray from 4.5)5-’-10 the bubble using the band emissivity derived by Raymond et al. /31/ JBund-)~fA8and(T, a )n2ds.
(8)
We show in Figure 5 the surface brightness in two bands: L-band (0.155 - 0.284 keV) and N-band (0.5~ - 0.873 keY). The predicted surface brightness from this model is -‘-IO8erg s~ cm2 srt in L-band and -‘-3x lO9erg s~ cm2 sr~ in ft-band. Although this corresponds to the value observed from outside the bubble, the surface brightness received in the bubble would not be largely different from that observed from outside. On the other hand, the observed counts rates by Wisconsin’s group /14/, 80 - 200 counts s~ (in L-band), and 30 - 50 counts s~ (in H-band), are deconvolved to the intrinsic surface brightness with use of the effective area data /7/ as (5—13)xlO9erg s~ cm2 sr1 (in L-band), and (1—2)x IO8erg ~ cm2 sr~ (in M-band). Compared between the observation and the model, although the surface brightness in M-band is not sufficiently explained about factor 3, X-ray in L-band is well explained as the superbubble origin. We conclude that the soft X-ray
114
K. Tomisaka
(~uDau~(p)d 0’ (5
D I
I
I
I
I
I
~//
-—
4
/~
~ -
(w2a)d
r
~‘
4)
£
~
0 (00.”’’’’
~0
(5
,
—‘--~
—‘~
—~
—
-~
—
.0 -d r’~ ~
-— 1-
-d00
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so
ax
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o
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~——w 04.-In
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0 0 0~
.-°‘n~
~
.0(0
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U)
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“.
—
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U)
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-
‘ ~
a)
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‘
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~ 0110
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4-
3 ‘U
4)
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;..~5
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—
0 (5 (5
(5 4)
~fl0..J.J
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0
,,:,,
0
5
.5) N 0
:3
ri-i
ii
Cycling of the LISM
(a)
700 600
IfiwIZ— 72x 144 ORNOZ= 10.ON 10.0 SCALE HEIGHT- 124.0 EXPL HEIGHT= 100.0 MESH (Z—01 35
500
N.J
I
I
(b)
X-RAT SB IL) s~aorHINoI TIME= 6501404 (YR)J STEI2= 3066
=
115
700
P~X-BA1 SB CM) TIME= (YB) BOO STE~= 6501404 3066 119x17= 72x
-
500
—
LOOtO= 1: ~
400
144
0RNDZ= jfl.0i 10.0 SCALE HEIGHT- 124.0 EXPL HEIGHT= 100.0 MESH IZ—0l 35 LOGtO=
—9.655 —9.
:~:~
N.J
400
300
.0’
300
—7- ~
100•
100•
o -—
-—-
—100
—100
—200
—200
—300
—300 0
200
100
300
H
400
0
100
200
3
Fig. 5. The surface brightness of X—ray emitted from the hot gas contained in the cavity of the superbubble. This is the case of n(z0)’0.3 cm3 and zoB=lOO pc. The surface brightness in L—band (0.155—0.284 key) and M—band (0.533—0.873 key) are are plotted in (a) and (b), respectively.
-‘4 ‘.,~
-t ~0
Ia-I
.
-7-
\O
flo
(cm3) ~0~,
—‘4 SO
Id2
102
Io~ r
I
00’ —8- 481j
200
—- -
—10. S~4
6, —~.417
200
0
—to
7~
~
6’ —8- S98
-
t-
(yr)
Fig. 6. Constraints on the fl-T plane by the conditions: LX ~ erg s-1, 1~> ~ K, and E
los
116
K. Tomisaka
background radiation is emitted from the local superbubble as well as the Sun.
the
SNR
surrounding
4. DISCUSSION
4.1 Excess X-ray Emission from the Galactic Ridge in 2
-
Ii keV Band
SNRs exploding in the cavity of superbubble are characterized by (1) a young age as yr (equation (4)) and (2) high temperature of the post-shock gas as ~
K.
(9)
The excess emission from the galactic ridge in the energy band of 2 — 10 keY, which was pointed out by Worrall et al. with the data of HEAO I /32/, has been reinvestigated by HEAO 2, EXEXSAT, and Tenma satellite /33/. It is found that the total luminosity in 2-11 key in our Galaxy attains ~~1038erg s~ - Because highly ionized iron line was detected by Tenma satellite, the excess emission is confirmed from hot gas with temperature -‘-1 keY. The proper candidate is a young SNR. However, radio SNRs or other feature related to SNRs are not observed in the field of view. Here, we discuss the model that the excess emission is from the /34/. For the early SNR to escape from radio survey, the radio lower than the detection toward the galactic i.e., The theoretical model limit for the surface brightnessridge, - diameter established. Thus, we use the empirical E—D relation explicitly density a /35/ as E(1GHz)~~2.88x104(.j~P.~_y38 n2
SNRs born in superbubbles surface brightness should be20Wm2 Hz~sr1 E(1GHz)~10 (1—D) relation has not been depending on the ambient
W m~2 Hz~ sr*
(10)
We plot in Figure 6 the region for age r, and the ambient density a which satisfies the condition Lx~1033 erg s~,T 7 K, and E’i1020W m2 Hz-I sr~ - SNRs in the low-density region as n-’-0.01 cm3 emits 4.10 the X-ray of 1O~ erg s~ during -‘-3x104 yr with radio surface brightness ~i1O’-0Wm~Hz~sr1 - Total luminosity emitted in 1.5 -25 keY in our galaxy becomes
Lx~iO.5x I 0~
erg s1 (for flQ .01 cm3),
(11)
where At is the mean interval of supernova explosions in our galaxy. We can conclude that ~Rs expanding in tenuous medium like a cavity of the superbubble fall below the detection limits of current radio surveys but still contribute significantly to the observed X-ray flux in the 2 - 11 keY band, if the supernova rate is as one per 10 years. 4.2 Picture of the Cycling of LLS’-I From the results of the numerical simulation on the superbubble, it has been found that the hot gas around our Sun seems to be a part of the cavity of a superbubble. The superbubbles are formed by the energy emitted from OB associations. It is observationally confirmed that 08 associations are associated with giant molecular clouds or molecular cloud complexes /36/. Further, the early type stars in the 08 association are formed in the giant molecular cloud in consequence of active early-type-star formation in it /37/. OB associations and giant molecular clouds are concentrated on spiral arms in the galaxy /38/. The ‘density wave promotes the coagulation of small clouds into large cloud complexes by what appears to be a combination of collisional agglomeration and large-scale gravitational instabilities /39/. This explains naturally the distribution of giant molecular clouds, because clouds are gathered into the spiral arms and giant molecular clouds are formed in the arms by collisional agglomeration and instabilities. type stars in OB associations formed by active star formation in giant molecular clouds explode sequentially as type II supernovae after several millions years have passed. Giant molecular clouds are destroyed under the influence of the active star formation, in
Early
the time scale --.io~ yr /40/. The formed 08 association emits large energy in the form of supernova explosions in -..(I--3)x io~ yr. In consequence, the interstellar matter in the vicinity of the OB association is heated-up by the shock fronts of SNRs. After that, the supernova rate decreases due to the relatively long lifetime of intermediate-mass stars. The superbubble does not expands further. After the active phase of the the heated matter return to the stancklrd interstellar matter?
superbubble,
how
does
The cooling time of hot gas in the cavity is estimated as
5/2xn
2 ~ 5O0kT An
8~
a
—I
(-j~~) yr. T .6
12
Cycling of the LISM
117
This is somewhat longer than the time necessary for interstellar matter to travel from one arm to the other arm tc;r-7r/(cZ~-qp)=2.7x108 yr, with the standard two-arm spiral model (the pattern velocity, Q~,=13.5km s kpc~, and the rotation velocity, 9-24.7km s~ kpc~). The superbubble should be destroyed by other processes: (1) Interstellar clouds permeate the cavity of the bubble and eventually fill up it. This timescale is expressed with the random velocity of clouds, v~j, as — r~ 3xIO~~—~—--’’ Vrar4 \-.J 3 1”8kni s~’ yr. c1— “200Pc (2) Galactic differential rotation deforms the shape of the bubble and squashes it. This phenomenon occurs in a timescale of ~
(14)
where R represents the distance from the galactic center, -‘- 10 kpc. Because the latter two timescales, t~ 1, and t~104.~ , are much smaller than ~ , the local interstellar matter will be mixed with the interstellar matter outside the bubble before reaching the next arm. Thus, the interstellar matter repeats the cycle. The author would like to acknowledge Professors S. Sakashita, Y. Uchida, and S. Ikeuchi for their encouragement. He also acknowledge Yamada Science Foundation and Nukazawa Memorial Foundation (Hokkaido University) for travel support. The numerical calculation was performed by HITAC M28O-H/t~200-Hat the Computing Center, Hokkaido University and FACON M38O-R at Tokyo Astronomical Observatory. This work was supported in part by Grant-in—Aid for Encouragement of Young Scientists from the Ministry of Education, Science, and Culture (61790072). He also acknowledges the JSPS Fellowships for Japanese Junior Scientists for financial aid (FY 1966).
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